Prove that f is a surjection. This is actually a consequence of the Fundalmental Theorem of Arithmetic, Theorem 8.16.

I don't know what the fact that a number is prime or the product of prime numbers has to be with solving the surjection.

You know that if that it may be represented as the product of primes , right? Well, except for every prime is odd. So, we could for the sake of convenience write every integer as where may be zero of course. But, as previously mentioned since every other prime is odd and the product of odd numbers is odd it follows that for some , right? So now what?

You know that if that it may be represented as the product of primes , right? Well, except for every prime is odd. So, we could for the sake of convenience write every integer as where may be zero of course. But, as previously mentioned since every other prime is odd and the product of odd numbers is odd it follows that for some , right? So now what?